Gabriel practices for a local marathon. If the
marathon is 42.195 kilometers long, how
many miles does Gabriel need to run in order
to condition himself? Round the answer to
the nearest tenth.
(1 mile ≈ 1.61 kilometers)

Answer:576 minutes

Step-by-step explanation:

The power as a product of powers can be rewritten  (2ax)³ as  (2ax )(2ax)(2ax )

Multiplication is the mathematical operation that is used to determine the product of two or more numbers.

The product can be defined as the multiplication operation of two or more terms so that another term can be gotten the same as the one that is been given that we were asked to rewrite.

Power is defined as the degree that is been found on the terms, the degree that can be on the term is 3, then it can be expressed in three terms

Therefore, the given expression is (2ax)³ can be rewritten as;

(2ax)³ =  (2ax )(2ax)(2ax )

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The mean of all exam scores in the class is found = 71

Normally distribution

A normal distribution is an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off symmetrically toward either extreme.

While data points are referred to as x in a normal distribution, they are called z or z-scores in the z-distribution. A z-score is a standard score that tells you how many standard deviations away from the mean an individual value (x) lies: A positive z-score means that your x-value is greater than the mean.

The z-score is found by;

z = (x - μ)/σ

x =  sample mean

μ =  mean score

σ =  standard deviation

Now, from this,

x = zσ + μ

For p = 80th percentile= 0.8, see z value from z score table.

z = 0.85

x = 85 points

85 = 0.85σ +  μ  .....eq 1

For p = 30% = 0.3, see the z value from the z score table.

z = -0.3802

x = 65

65 = -0.3802σ +  μ  .....eq 2

Solving eq 1 and 2.

σ = 16.25

Put in eq 1

μ = 71.19

μ = 71

Thus, the mean of all exam scores in the class is found = 71

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Answer:

probability is 1.

Step-by-step explanation:

In a lot of probability problems when asking for “at least two” is usually easier to see the opposite case, that is, the “none of them” case…

P(“at least one … X”) = 1 - P(“none of them … X”)

I will we exclude 29th of February, that is, considering none of the people was born on the leap day of a leap year.

First, let’s see what happens for 2 people. We can name one of those 2 people as “first” and the other as “second”. Whatever the birthday of the “first” one is, the other has 364 out of 365 days in the year to have a different birthday.

p(2) = 1–364/365 = 1/365

For 3 people, the “first” has a birthday, the “second” has a probability of 364/365 to have a different birthday and the third has a probability of 363/365.

p(3) = 1 - 364/365 * 363/365= (365^2 - 364*363)/365^2

For 4 people:

p(4) = 1 - 364/365 * 363/365 * 362/365

…

For n people, if n is less than 366:

p(n) = 1 - (364! / [365 - n]! )/365^(n-1)

p(n)=1−364!(365−n)!⋅365n−1

Obviously, if n is 366 or more, since we excluded the leap day there must be always 2 people with the same birthday (pigeonhole principle), and then in this cases the probability is 1.

Answer

x=10.

Step-by-step explanation:

-2.3x-4.2x=-66.3

-2.3+-4.2=-6.5x

-6.5x÷-6.5

-66.3÷-6.5

x=10.

Answer: 333 Cookies

Step-by-step explanation:
Let E = Cookies by Esther
Let L = Cookies by Lee
The equation for amount of cookies: E+L

L=141
E=L+51
Substitute L
E=141+51=192
E+L=141+192=333

Answer:

[tex]10 \div x - 10 \div (x - 1) = 30[/tex]

Answer:

A,) 20

Step-by-step explanation:

First, I am assuming that the problem is 5k = 100, not "5k = 100k =" as it was written.

We need to end up with "k equals some number."  This is called solving for k.  In order to do this we need to have k by itself.  We look at the problem and ask, "what is preventing k from being by itself?"  In this case k has a "times 5" with it.  How can we get rid of that?  Well we can do the opposite of "times 5,"  and that is to divide the left side by 5.  That leaves k by itself which is exactly what we need.  But if do something to one side of an equation, we need to do it to the other side for the equation to still be true.  So in this case we also have to divide the right side by 5 also, which gives us 20 on the right side.  So in our original problem:

5k = 100

Divide both sides by 5 and we have the answer:

k = 20

We will see that the largest number is 9/12, and Russ ate 9/12 of his pizza, so he is the one that ate most of his pizza.

Here we know that:

So we just need to see which of the given numbers is the largest one.

We can rewrite the fractions as:

2/3 = 0.66

3/5 = 0.6

9/12 = 3/4 = 0.75

The largest number is 0.75, in this way we conclude that Russ is the one that ate more pizza.

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Using inequality, we can conclude that maximum of 14 people can visit the amusement park.

So, (p) a maximum number of people who can visit the park:

Now, calculate as follows:

Therefore, using inequality, we can conclude that maximum of 14 people can visit the amusement park.

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Answer:

180

Step-by-step explanation:

9x20

Answer:

yes that is the correct answers

There are 60 boys to make up the boys' teams and 40 girls to make up the girls' teams.

We are also told that the teams should be the same size.

This means that irrespective of the number of teams, each team should contain the same number of players.

Thus, the largest number of people that can be placed on a team is;

The highest common factor ;

The HCF is 10 x 2 = 20, therefore;

The largest number of people that can be placed on a team is 20.



a)P(all seniors) =(25C3)/(30C3) =0.5665

b)P(All Juniors)=(5C3)/(30C3) =0.0025

c)P(2 senior and 1 Junior) =(25C2)(5C1)/(30C3) =0.3695

d)P(1 senior and 2 Junior) =(25C1)(5C2)/(30C3) =0.0616

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Answer:

Answer:The area of the triangle is 60 in.

explanation:

Because we have 6inches in the weigth and 5inches in the height .

Answer:

AC=8

Step-by-step explanation:

2x=2(8)

2x=16

x=16÷2

x=8

Answer:

they're similar

Step-by-step explanation:

hello again ;)

A graph of the image of triangle V'W'X' after a rotation of 90° counterclockwise about the origin is: graph A.

A rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

In Geometry, rotating a point 90° about the origin in a counterclockwise (anticlockwise) would produce a point that has the coordinates (-y, x).

Note: Each interval on this graph represents 1 unit.

By applying a rotation of 90° counterclockwise to triangle VWX, the coordinates of the vertices of the image triangle V'W'X' include the following:

(x, y)                    →            (-y, x)

Point V = (-2, -4)   →     Point V' = (-(-4), -2) = (4, -2)

Point W = (-2, -2)   →    Point W' = (-(-2), -2) = (2, -2)

Point X = (-5, -4)   →  Point X' = (-(-4), -5) = (4, -5)

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The test statistic for this hypothesis test is; t = 1.5

The formula for test statistic is;

t = (x' - μ)/(σ/√n)

where;

x' is sample mean

μ is population mean

σ is standard deviation

n is sample size

We are given;

Sample mean; x' = 8.12 hours

Population mean; μ = 8 hours

Standard deviation; σ = 0.72 hours

sample size ; n = 81 pilots

Thus;

t = (8.12 - 8)/(0.72/√81)

t = 0.12/0.08

t = 1.5

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If grace and jack are playing a game with a gigantic bucket of markers. The probability are  yellow 0.24,  blue 0.74,  red 0.02.

Given data:

Yellow markers = 12

Blue markers =37

Red marker =1

Total number of markers = 12 + 37 + 1

Total number of markers = 50

Probability of an event occuring= Favorable number of outcomes / Total number of outcomes

Probability of getting an yellow marker = 12/50

Probability of getting an yellow marker = 0.24

Probability of getting an blue marker = 37/50

Probability of getting an blue marker = 0.74

Probability of getting an red marker = 1/50

Probability of getting an red marker = 0.02

Probability model

Type of maker  Frequency Probability

Yellow                     12             0.24

Blue                         37              0.74

Red                           1              0.02

Therefore the probability are  0.24, 0.74, 0.02.

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Using proportions, the coordinates of the point that divides directed line segment YX so that the ratio of YP to PX is 5 to 3 are given by:

[tex](x,y) = \left(\frac{3}{8}(x_y - x_x) + x_x, \frac{3}{8}(y_y - y_x) + y_x\right)[/tex]

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations such as multiplication or division from the given ratios.

Division of line segments is one application of proportions. The entire length of the line segment with endpoints XY is given by:

Y - X.

Now we have point P, dividing the line segment YX so that the ratio of YP to PX is 5 to 3, meaning that XP is 3/8 of XY, that is:

[tex]P - X = \frac{3}{8}(y - x)[/tex]

Then the x-coordinate of P is found as follows:

[tex]x - x_x = \frac{3}{8}(x_y - x_x)[/tex]

[tex]x = \frac{3}{8}(x_y - x_x) + x_x[/tex]

The y-coordinate is found applying the same rule with the y-coordinates of points X and Y, as follows:

[tex]y - y_x = \frac{3}{8}(y_y - y_x)[/tex]

[tex]y = \frac{3}{8}(y_y - y_x) + y_x[/tex]

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The value of x for quadratic equation f(x) = 2x² + 3x when f(-5) is 35.

Given, f(x) = 2x² + 3x

To find: f(-5)

For the quadratic equation f(x) = 2x² + 3x substitute the value -5 in place of x as the f(-5) has been mentioned in the question.

So,

f(-5) = 2(-5)² + 3(-5)

A Square of -5 is 25 and 3 multiplied by -5 is 15,

f(-5) = 2(25) + (-15)

Multiple of 25 and 2 is 50 subtracted by 15,

f(-5) = 50 - 15

At last, subtract 50 by 15,

f(-5) = 35

∴ For equation f(x) = 2x² + 3x when f(-5), the value of x = 35.

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Answer:

The radius is from the middle to the edge, in this case it looks the radius is 4

The volume of the cone has a value of 410.67 cubic meters

From the question. the height and the radius of the cone are given as

Height = 7 feet

Radius = 8 feet

The volume of the cone can be calculated using the following volume formula

Volume = 1/3πr^2h

Substitute the known values in the above equation

So, we have

Volume = 1/3 * 22/7 * 8 * 7^2

Evaluate the products

Volume = 410.67

Hence, the volume is 410.67 cubic meters

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4.372 × [tex]10^{13}[/tex] more kilograms the mass of the Antarctic iceberg than the mass of the Rock of Gibraltar.

Mass of the Antarctic iceberg = 4.55 × [tex]10^{13}[/tex]  

Mass of the rock of Gibraltar  = 1.78 × [tex]10^{12}[/tex]  

Excessive mass of Antarctic Icebergs than the rock of Gibraltar,

4.55 × [tex]10^{13}[/tex]  - 1.78 × [tex]10^{12}[/tex]  

Subtract easily both should be in the same power of ten,

= 4.55 × [tex]10^{13}[/tex]  - 1.78 × [tex]10^{12}[/tex]  

= 43.72  × [tex]10^{12}[/tex]  

= 4.372 × [tex]10^{13}[/tex]

Scientific notation is used to express quantities that are either too large or too little to be represented by decimals. Scientific format, standard index format, and standard format are other terms for the same thing.

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Step-by-step explanation:

a probability is always

desired cases / totally possible cases

28 students in total.

6 are female.

so, we have 28-6 = 22 male students.

7 of the 28 students have an A.

17 male students do not have an A.

that means 22-17 = 5 male students have an A.

and that means 7-5 = 2 of the female students have an A.

"given that they have an A".

that reduces our totally possible cases to 7.

the probability that an A-student is male is therefore

5/7 = 0.714285714...

and FYI

the probability that an A student is female is

2/7 = 0.285714286...

The probability that a student is male given that they have an A is approximately 0.538.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

We can use Bayes' theorem.

P(male | A) = P(A | male) x P(male) / P(A)

We are given:

P(A | male) = 7/17

(7 students are male and have an A, out of 17 male students)

P(male) = 17/28

(17 students are male, out of 28 total students)

P(A) = (6+7) / 28

(13 students have an A, out of 28 total students)

Plugging in these values.

P(male | A) = (7/17) x (17/28) / (13/28) = 0.538

Therefore,

The probability that a student is male given that they have an A is approximately 0.538.

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40

Explanation

Step 1

a)initially we have 8 dots

after that

in step 2, we have a new row and , now there are 8 dots per row, so

in step 3, we should have

and

as we can see, the rule works

Step 2

now, to find the patter in step 4, just apply

and

finally, to know the number of dots

Multiply the number of row, by the number of dots per row, so

therefore, the answer is 40

I hope this helps you

The sandwich's price is represented by the variable s , 2 is the coefficient of s and 2.97 represents both the cost of a big drink and a constant

What is  Algebraic Expression?

An algebraic expression is one that has been constructed using integer constants, variables, and algebraic operations. For instance, the algebraic formula 3x2 2xy + c

The cost of Andrew's lunch is written as the algebraic expression

2s + 2.79 as a given. He bought a huge drink and two sandwiches.

In the algebraic expression given;

2s + 2.79

Here, 2 stand in for the coefficients of s, which stands for the quantity of sandwiches he purchased.

The sandwich's price is represented by the variable s, which is a function of the coefficient.

And 2.97 represents both the cost of a big drink and a constant since no further letters have been added.

Hence, sandwich's price is represented by the variable s , 2 is the coefficient of s and 2.97 represents both the cost of a big drink and a constant

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1) the equation is:

So we can rewrite the equation as a slope intercept so:

So the slope is -1/2

2) the equation is:

Now we evaluete the coordinates to see which one is not on the line so for (1,-1)

So is on the line

for (-1,-4)

So it is on the line

for (3,2)

So it is on the line

Finally for (1,2)

So (1,2) is not on the line

3) if the slope is -2 and goes to the point (3,-1) we can use the equation of a line to find the intercept so:

So the intercept is 5 so the equation is:

Answer:

Yes

Step-by-step explanation:

Parallel lines are 2 lines that go in the same direction that will never touch each other.

Hope that helps